Amplification, attenuation, and dispersion of sound in inhomogeneous flows

First order effects of gradients in nonuniform potential flows of a compressible gas are included in a dispersion relation for sound waves. Three nondimensional numbers, the ratio of the change in the kinetic energy in one wavelength to the thermal energy of the gas, the ratio of the change in the total energy in one wavelength to the thermal energy, and the ratio of the dillatation frequency (the rate of expansion per unit volume) to the acoustic frequency, play a role in the separation of the effects of flow gradients into isotropic and anisotropic effects. Dispersion and attenuation (or amplification) of sound are found to be proportional to the wavelength for small wavelength, and depend on the direction of wave propagation relative to flow gradients. Modification of ray acoustics for the effects of flow gradients is suggested, and conditions for amplification and attenuation of sound are discussed

Nonclassical acoustics

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows

Wave theory of turbulence in compressible media (acoustic theory of turbulence)

The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation

Wave theory of turbulence in compressible media

An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease

The content of nitrogen compounds in the Wel river in the light of the Nitrates Directive

In this paper, the results of the research are presented on the content and transformation of nitrogen compounds in the Wel River (the largest tributary of the Drwęca River). The catchment area of the studied river is predominantly agriculturally developed. Along the river course, 6 sample collection sites were selected, situated in places with different land development of the drainage basin. The average concentration of total nitrogen in the water of the Wel River amounted to 1.807 mg/dm 3, mineral nitrogen - 0.557 mg/dm 3 and organic nitrogen - 1.250 mg/dm 3. The organic form of nitrogen dominated at all sites (the average content for the whole river amounted to 69%). Nitrate nitrogen dominated in the pool of mineral nitrogen. The lowest concentrations of nitrates were being recorded at lakeland sites, whereas the highest - at two terminal sites situated within the lower reaches of the river, where the drainage basin has a typically agricultural character

The content of nitrogen compounds in the Wel river in the light of the Nitrates Directive

In this paper, the results of the research are presented on the content and transformation of nitrogen compounds in the Wel River (the largest tributary of the Drwęca River). The catchment area of the studied river is predominantly agriculturally developed. Along the river course, 6 sample collection sites were selected, situated in places with different land development of the drainage basin. The average concentration of total nitrogen in the water of the Wel River amounted to 1.807 mg/dm3, mineral nitrogen - 0.557 mg/dm3 and organic nitrogen - 1.250 mg/dm3. The organic form of nitrogen dominated at all sites (the average content for the whole river amounted to 69%). Nitrate nitrogen dominated in the pool of mineral nitrogen. The lowest concentrations of nitrates were being recorded at lakeland sites, whereas the highest - at two terminal sites situated within the lower reaches of the river, where the drainage basin has a typically agricultural character

A systematic review on the barriers and facilitators to physical activity in informal / unpaid carers worldwide

What are the barriers and facilitators to physical activity in unpaid / informal carers in the UK

A systematic review on the barriers and facilitators to physical activity in informal / unpaid carers in the UK

What are the barriers and facilitators to physical activity in unpaid / informal carers in the UK